Date: Jan 31, 2013 3:23 AM
Author: William Elliot
Subject: Re: Beating the Odds?
On Wed, 30 Jan 2013, forbisgaryg@gmail.com wrote:

> On Wednesday, January 30, 2013 12:29:09 AM UTC-8, William Elliot wrote:

> > There is a fair coin with a different integer on each side that you can't

> > see and you have no clue how these integers were selected. The coin is

> > flipped and you get to see what comes up. You must guess if that was the

> > larger of the two numbers or not. Can you do so with probability > 1/2?

>

> Well, there was the monty hall problem years ago. Suppose there are 3

> keys and you have to choose one. One of the three turns on a car's engine

> where the other two do not. After you choose a key Monte takes one and

> tries it in the car and it doesn't turn over the engine. He then asks

> you if you'd like to change your mind. What should you do? You should

> change your mind because the first key you chose had a one in three chance

> of turning on the car where the remaining key has a two in three chance.

>

> Soo...

>

> Assuming the coin only has positive integers then you should guess

> the number showing is the smaller integer because there are more

> integers greater than x than there are less than x and this is true

> for all positive integers x.

>

Recall, you have no clue how the integers were selected much less that

both are positive or non-negative.

Here's a variant. Instead of integers, the coin has

a positive rational on each side.